Harvey's center is expected to move off the coast Monday, but rains likely will continue pummeling the region through Friday, the National Hurricane Center said Sunday evening.

The storm has devastated Texas, destroying buildings and causing widespread power outages and massive flooding.

Houston is under a flood warning after a "deluge" of intense rain hit the city overnight Saturday. The city's emergency services are at capacity, and the William P. Hobby Airport has canceled all inbound and outbound flights.

Parts of the Houston area may see as much as 50 inches of rainfall, according to the National Weather Service.

The exact death toll is unclear, but the National Weather Service reports five people have died in the Houston area.

Authorities urge citizens to stay off the streets and to climb to rooftops if they are trapped.

HOUSTON ― Two days after Hurricane Harvey made landfall in southern Texas, the city of Houston is facing life-threatening, catastrophic flooding that authorities warn could be "historic."

The National Hurricane Center said Sunday evening that the storm's center was moving southeast and would continue to do so for the next two days. Harvey is expected to "move off the middle Texas coast on Monday and meander just offshore through Monday night," the center forecasted.

But catastrophic rains are expected to continue plaguing the Texas coast through Friday, and those in Houston and other affected areas should not attempt to travel if they're in a safe place, the NHC warned.

Earlier on Sunday, the National Weather Service reported that while winds were decreasing and Harvey has been downgraded to a tropical storm, heavy rainfall is creating life-threatening hazards across much of Texas' southeast. The service is predicting as much as 50 inches of rain could fall in some parts of the region as the slow-moving storm hangs over the state.

NWS meteorologist Patrick Burke told HuffPost that the tropical storm is now stationary, and close enough to the water that it has an unlimited source of fuel. He warned that the weather event will affect the area for "days, if not weeks."

There was also some concern that Harvey could make a potential second landfall, as some models predict the storm moving back over the Gulf of Mexico and gaining strength before striking land again.

"If you're sitting in the Houston area and you see a break and the rain lets up, don't let your guard down. It's gonna come right back in," Burke said. "Rainfall predictions are as high as we've ever made for a storm."

Authorities also issued a tornado watch for southern Houston on Sunday, with emergency services telling those in the affected area to hunker down in place and keep away from windows. The NHC additionally put parts of the Texas coastline under Tropical Storm Watch as of early Sunday evening, and declared several more tornado warnings for towns near the area.

David Lohr/HuffPost
Firefighters with the Houston Fire Department check on a submerged vehicle off Interstate 10 in Houston&nbsp;on Sunday.

The exact death toll from the storm remains unclear as rescue workers struggle to reach affected areas, but the National Weather Service reported Sunday that five people have died in the Houston area.

Houston Mayor Sylvester Turner has urged residents to prepare for days of heavy rains and flooding. During a press conference on Sunday morning, Turner advised residents to stay in place and said the city would be opening more shelters to cope with the effects of Harvey. The city is opening its George R. Brown Convention Center as one such storm shelter, and Dallas will open its Kay Bailey Hutchison Convention Center on Tuesday morning.

"Just stay put," Turner pleaded. "We need you to help us."

Turner also told residents to refrain from driving and to "stay off the streets unless it's an emergency."

David Lohr/HuffPost
A submerged car in Katy, Texas, during the storm. Authorities are urging people to stay off the roads.

A number of highway feeder roads were flooded just west of Houston on Sunday afternoon, and police had blocked roads to surrounding rural areas, where ranches and farms were also under several feet of water.

Electric signs on Interstate 10 traveling east into the city read "High water" and urged drivers to "Turn around, don't drown."

Members of the Houston Fire Department were out searching the interstate for both trapped drivers and bodies on Sunday afternoon. They commandeered a HuffPost reporter's boat to look for a woman trapped in her car. When a rookie fireman asked if they would be recovering bodies, another explained they were only picking up survivors on this pass.

Some residents with access to boats carried out their own rescues. Numerous videos showed citizens filling their private boats with evacuees and ferrying them to safety.

Officials urged residents trapped in their homes to avoid sheltering in their attics and to get on their roofs instead. "[H]ave reports of people getting into attic to escape floodwater," Houston Police Chief Art Acevedo warned Sunday morning. "[D]o not do so unless you have an ax or means to break through onto your roof."

The city's emergency services also tweeted that they were at capacity and asked residents to only call if they faced imminent danger. The mayor also advised people to give preference to life-threatening situations when calling 911.

Officials said the city's public hospital, Ben Taub, was evacuated Sunday due to flooding and power outages. Later in the day, Bayshore Medical Center, another Houston metropolitan area hospital, decided to suspend operations and evacuate its 196 patients.

David Lohr/HuffPost
A partially submerged speed limit sign in Katy, Texas, shows how high the floodwaters have reached in some areas.

Houston's emergency services had responded to 2,500 calls since midnight on Sunday, Turner stated during his Sunday morning press conference. There have been 250 rescues since Saturday night, the mayor said, all of them from vehicles.

The mayor defended the decision not to issue an evacuation order for Houston, saying it would have created "a nightmare." Turner had cautioned residents against leaving the city on Friday: "Please think twice before trying to leave Houston en masse. No evacuation orders have been issued for the city."

Texans received mixed messages from officials regarding evacuations in the lead-up to the storm. Gov. Greg Abbott (R) issued a statement on Friday advising Houston residents to evacuate north even if no local order to do so was in place.

Abnormally intense rains and flooding have battered Houston and the surrounding area in recent years. Last April, the area was soaked by what the local flood control district deemed a one-in-10,000 year rainfall event as 15 inches of rain poured in some parts of Houston in just 24 hours. In May 2015, at least six people died and more than a thousand vehicles were submerged when 12 inches of rain fell in just 10 hours.

The Houston area experienced similar rainfall totals in July 2012. Before that, the area hadn't been pummeled by such weather since the 1960s, the Houston Chronicle wrote last summer.

The rain on Sunday easily topped previous years heavy rains, however, with the National Weather Service reporting parts of Houston getting more than 30 inches of rain in the past 48 hours.

Rockport Mayor C. J. Wax confirmed the death of a man who was trapped in his burning house, unable to be reached by rescuers during the height of the hurricane. Wax said at least 12 other people sustained injuries.

The Coast Guard said Sunday that it had rescued 32 people in distress at sea, according to The New York Times.

More than 300,000 people across Texas were without power on Sunday, according to the Electric Reliability Council of Texas. Abbott said in a press conference Sunday afternoon that 250 state highways were closed and 3,000 national guard and state guard members had been deployed.

Brock Long, administrator of the Federal Emergency Management Agency, appeared on CNN Sunday morning, warning that the disaster in Texas would be "a landmark event."